A Unified Framework for Analyzing and Optimizing a Class of Convex Fairness Measures

Fairness concerns arise naturally across a wide range of decision-making contexts and application domains. Addressing these concerns requires integrating fairness measures into optimization models; however, quantifying fairness, as well as formulating and solving fairness-promoting optimization problems, remain significant challenges. In “A Unified Framework for Analyzing and Optimizing a Class of Convex Fairness Measures,” M. Y. Tsang and K. S. Shehadeh propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures. They introduce a unified framework for optimization problems with a convex fairness measure objective or constraint, including unified reformulations and solution methods. Additionally, they establish mechanisms for quantifying the impact of employing different convex fairness measures on the optimal solutions to the resulting fairness-promoting optimization problem. Numerical experiments, including applications to resource allocation and facility location, demonstrate the computational efficiency of the unified framework over traditional ones.